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Variables and Expressions
Unit 1 Lesson 1
VARIABLES AND EXPRESSIONS
Students will be able to:
write mathematical expressions for verbal expressions,
and vice versa.
Key Vocabulary:
Variables Power
Algebraic Expression Base
Factors Exponent
Product
VARIABLES AND EXPRESSIONS
VARIABLES are symbols used to represent unspecified numbers or values. Any letter can be used as a variable.
𝒙, 𝒚, 𝒛, 𝒂, 𝒓, 𝒅, 𝒔
VARIABLES AND EXPRESSIONS
ALGEBRAIC EXPRESSION consists of one or more numbers and variables along with one or more arithmetic operation.
Various ways to represent a product of 𝒙 and 𝒚:
In each expression above, the quantities being multiplied are called factors, and the result is called the product.
𝟔𝒚, 𝟕𝒙 − 𝟑, 𝟗 +𝒓
𝒔, 𝒌 ⋅ 𝟓𝒋, 𝟓𝒂𝒃 ÷ 𝟑𝒄𝒅
𝒙𝒚, 𝒙 ⋅ 𝒚, 𝒙 𝒚 , 𝒙 𝒚, 𝒙 𝒚
VARIABLES AND EXPRESSIONS
Translating Verbal Expression into Algebraic Expression:
Addition Subtraction Multiplication Division
Plus Minus Times Divided Sum of Difference between/of Product of Quotient of
More than Less than Multiplied by Ratio of Increased by Decreased by Per
Combined Fewer than Out of Together percent Total of
Added to
VARIABLES AND EXPRESSIONS
Translating Verbal Expression into Algebraic Expression:
Example: three more than a number 𝒙
Verbal Expression: three more than a number 𝒙
Algebraic Expression: 𝟑 + 𝒙
VARIABLES AND EXPRESSIONS
Sample Problem 1: Write each expression algebraically.
a. The product of 8 and a number 𝒙
b. The difference between 16 and 𝒙 squared
c. The sum of 7 and 𝒎
d. 𝒙 divided by three
e. Four times eight plus 𝒏
VARIABLES AND EXPRESSIONS
Sample Problem 1: Write each expression algebraically.
a. The product of 8 and a number 𝒙 = 𝟖𝒙
b. The difference between 16 and 𝒙 squared = 𝟏𝟔 − 𝒙𝟐
c. The sum of 7 and 𝒎 = 𝟕 +𝒎
d. 𝒙 divided by three =𝒙
𝟑
e. Four times eight plus 𝒏 = 𝟒 𝟖 + 𝒏
VARIABLES AND EXPRESSIONS
POWER is an expression that represents repeated multiplication of the same factor.
where:
𝒙 = base
𝒏 = exponent, which corresponds to the number of times the base is used as a factors
𝒙𝒏
VARIABLES AND EXPRESSIONS
POWER is an expression that represents repeated multiplication of the same factor.
Symbol Words Meaning 𝟐𝟏 𝟐 to the first power 𝟐 𝟐𝟐 𝟐 to the second power 𝟐 ⋅ 𝟐 𝟐𝟑 𝟐 to the third power 𝟐 ⋅ 𝟐 ⋅ 𝟐 𝟐𝟒 𝟐 to the fourth power 𝟐 ⋅ 𝟐 ⋅ 𝟐 ⋅ 𝟐
𝟐𝟓 𝟐 to the fifth power 𝟐 ⋅ 𝟐 ⋅ 𝟐 ⋅ 𝟐 ⋅ 𝟐
𝟐𝒏𝟔 𝟐 times 𝒏 to the sixth power 𝟐 ⋅ 𝒏 ⋅ 𝒏 ⋅ 𝒏 ⋅ 𝒏 ⋅ 𝒏 ⋅ 𝒏 𝒙𝒏 𝒙 to the 𝒏th power 𝒙 ⋅ 𝒙 ⋅ 𝒙 ⋅ 𝒙 ⋅ 𝒙 ⋅ … ⋅ 𝒙
VARIABLES AND EXPRESSIONS
POWER is an expression that represents repeated multiplication of the same factor.
Example: 𝟐𝟔
Power: 𝟐𝟔 = 𝟐 ⋅ 𝟐 ⋅ 𝟐 ⋅ 𝟐 ⋅ 𝟐 ⋅ 𝟐 𝟐𝟔 = 𝟔𝟒 Base: 𝟐
Exponent: 𝟔 6 factors of 2
VARIABLES AND EXPRESSIONS
Sample Problem 2: Find each value.
A. 𝟑𝟐
B. 𝟒𝟑
C. 𝟓𝟐
D. 𝟔𝟐
E. 𝟐𝟒
VARIABLES AND EXPRESSIONS
Sample Problem 2: Find each value.
A. 𝟑𝟐 = 𝟑 ⋅ 𝟑 = 𝟗
B. 𝟒𝟑 = 𝟒 ⋅ 𝟒 ⋅ 𝟒 = 𝟔𝟒
C. 𝟓𝟐 = 𝟓 ⋅ 𝟓 = 𝟐𝟓
D. 𝟔𝟐 = 𝟔 ⋅ 𝟔 = 𝟑𝟔
E. 𝟐𝟒 = 𝟐 ⋅ 𝟐 ⋅ 𝟐 ⋅ 𝟐 = 𝟏𝟔
VARIABLES AND EXPRESSIONS
Translating Algebraic Expression into Verbal Expression:
Example: 𝟒𝒎
Algebraic Expression: 𝟒 ⋅ 𝒎
Verbal Expression: four times a number 𝒎
The product of 4 and 𝒎
VARIABLES AND EXPRESSIONS
Sample Problem 3: Write a verbal expression for each algebraic expression.
A. 𝟑 − 𝒕
B. 𝒚 + 𝟗
C. 𝟔
𝒔
D. 𝟒𝒛
E. 𝟐𝟏𝒅 − 𝟑
VARIABLES AND EXPRESSIONS
Sample Problem 3: Write a verbal expression for each algebraic expression.
A. 𝟑 − 𝒕 = the difference between 𝟑 and 𝒕
B. 𝒚 + 𝟗 = the sum of 𝒚 and 𝟗
C. 𝟔
𝒔 = the ratio between 𝟔 and 𝒔
D. 𝟒𝒛 = the product of 𝟒 and 𝒛
E. 𝟐𝟏𝒅 − 𝟑 = the difference between 𝟐𝟏 times 𝒅 and 𝟑